Problem: Divide the following complex numbers: $\dfrac{4 e^{13\pi i / 12}}{ e^{\pi i / 3}}$ (The dividend is plotted in blue and the divisor in plotted in green. Your current answer will be plotted orange.)
Solution: Dividing complex numbers in polar forms can be done by dividing the radii and subtracting the angles. The first number ( $4 e^{13\pi i / 12}$ ) has angle $\frac{13}{12}\pi$ and radius 4. The second number ( $ e^{\pi i / 3}$ ) has angle $\frac{1}{3}\pi$ and radius 1. The radius of the result will be $\frac{4}{1}$ , which is 4. The angle of the result is $\frac{13}{12}\pi - \frac{1}{3}\pi = \frac{3}{4}\pi$ The radius of the result is $4$ and the angle of the result is $\frac{3}{4}\pi$.